Question: Convert the following equation from standard form to slope intercept form. In other words, if the equation is rewritten to look like $y = mx + b$, what are the values of $m$ and $b$ ? $-2x - 3y = -2$
Solution: Move the $x$ term to the other side of the equation. $-3y = 2x - 2$ Divide both sides by $-3$ $y = -\dfrac{2}{3}x + \dfrac{2}{3}$ Inspecting the equation in slope intercept form, we see the following. $\begin{align*}m &= -\dfrac{2}{3}\\ b &= \dfrac{2}{3}\end{align*}$ Behold! The magic of math, that both equations could represent the same line! $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$